Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}5x+2y &= -6 \\ -8x-2y &= -5\end{align*}$
We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-3x = -11$ Divide both sides by $-3$ and reduce as necessary. $x = \dfrac{11}{3}$ Substitute $\dfrac{11}{3}$ for $x$ in the top equation. $5( \dfrac{11}{3})+2y = -6$ $\dfrac{55}{3}+2y = -6$ $2y = -\dfrac{73}{3}$ $y = -\dfrac{73}{6}$ The solution is $\enspace x = \dfrac{11}{3}, \enspace y = -\dfrac{73}{6}$.